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In triangle ABC, the line joining the ci...

In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then `cos A + cos C` is equal to

A

`(1)/(2)`

B

1

C

`sqrt3`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
The distance of circumcenter from side AC is `R cos B`, and the distance of incenter from side AC is r. Therefore,
`R = cos B = r " or " (r)/(R) = cos B`
`rArr 4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2) = cosB`
`rArr cosA + cos B + cos C - 1 = cos B`
or `cos A + cos C = 1`
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